(\partial)/(\partial y)((z)(3x+5y)^9)

解

\frac{\partial}{\partial y} ((z) (3 x + 5 y)^{9})

45 z (3 x + 5 y)^{8}

解答ステップ

\frac{\partial}{\partial y} ((z) (3 x + 5 y)^{9})

z, x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial y} ((3 x + 5 y)^{9})

連鎖法則を適用:

9 (3 x + 5 y)^{8} \frac{\partial}{\partial y} (3 x + 5 y)

= 9 (3 x + 5 y)^{8} \frac{\partial}{\partial y} (3 x + 5 y)

\frac{\partial}{\partial y} (3 x + 5 y) = 5

= z \cdot 9 (3 x + 5 y)^{8} \cdot 5

簡素化

= 45 z (3 x + 5 y)^{8}